A waveform inversion including tilt: Method and simple tests

Abstract

A new waveform inversion method is proposed to deal with horizontal seismograms strongly contaminated by tilt signals, without assumptions regarding tilt motions. Instead of decomposing the horizontal seismograms into translational and tilt contributions, we realize this task by calculating the Green's functions consisting of not only the seismometer's response to the synthetic translational motions but also to the synthetic tilt motions. A finite difference method (FDM), which uses a staggered grid and a perfect matched layer (PML) boundary condition, is used to calculate the Green's functions. This method enables calculation of wavefields which have wavelengths of up to 10 times larger than the dimension of the computational grid. Although reflected waves from the numerical boundaries are negligible, comparisons with analytical solutions evidence errors of up to several per cent. These occur either because the source-to-receiver distance is small once compared to the grid size, or as a consequence of the half-cell difference between the actual free surface and the station location. In addition, in the case that the free surface is not flat, an error of up to 60 per cent occurs in calculating the tilt motion, due to the stair-like approximation of topography in the FDM. This latter error can be reduced to 10 per cent by averaging the tilts at five adjacent cells aligned in the direction of the tilt component, centred on the target grid cell. By applying this algorithm, a waveform inversion can be used to successfully reconstruct the vertical and horizontal seismograms of very-long-period (10-30 s) pulses at Asama Volcano, central Japan, despite the fact that the horizontal seismograms are strongly contaminated by tilt signals. © 2010 The Authors Geophysical Journal International © 2010 RAS.